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Brexit leader Nigel Farage: Trump can pull off an upset win, like we did in the UK

Brexit campaign leader Nigel Farage, a vocal supporter of Donald Trump , told CNBC on Thursday the GOP presidential nominee is not as far behind as the polls show.

Like what turned the tide for the leave camp in Britain, Trump also needs to mine voters who have never showed up at the polls, Farage said. "Polling companies, both in Britain and America, now find it very difficult to measure non-voters who come into the process."

Farage appeared on "Squawk Alley" from Las Vegas, where he attended the third and final U.S. presidential debate on Wednesday night.

The former and now interim leader of the UK Independence Party also went to the second presidential debate in St. Louis earlier this month, and appeared alongside Trump at an August campaign rally in Mississippi.

Many supporters compare Trump's campaign to Britain's vote to depart the European Union in June — arguing the billionaire's true support has not been fully reflected in presidential polling, which favored Hillary Clinton before the third debate.

Britain's vote to leave the EU defied the polls. "The opinion polls can say what they say. [But] on Brexit day in Britain, the remain side were 10-points in the lead, and yet our side still won."

The biggest comparison between Trump and Brexit is that Clinton "campaigns on similar slogans to the stay-in-the-EU campaign," said Farage. "You got the establishment saying, 'Everything is fine. Trust us.'"

"[But] actually out there in middle England, and now here in middle America, there's a lot of people saying, 'You know what, the last few years I've seen the rich get richer and our lives have not improved. It's time for change,'" he said.

On the debate issues, he said "marginally [Trump] got the better on the night." He also said Trump did a better job keeping his temper in check, while making compelling cases on the economy and foreign policy.

He said Trump should try to make his refusal to commit to accepting the election outcome work for him.

"As an anti-establishment campaigner in Britain for two decades, I have seen the establishment in my country cheat," he said. "I understand Trump's frustration, taking on the establishment. But I would suggest this to Donald Trump, he needs to move it on."

Trump should say something like win or lose he would "drain the swamp" and work for election reform in America, Farage said. "Then he can turn that comment a little positive."

Earlier Thursday , campaign manager Kellyanne Conway defended Trump's rigged election comments, saying a vow to adhere to an outcome of voting that has not been "verified" and "certified" is "insane."